Finite Group Databasebeta

← #19143435

Subgroups — #19143435

Order 5504.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063354C211yesmaximal, characteristic
2#14583378C211yesmaximal, characteristic
3#14583375C211yesmaximal, characteristic, complemented
4#14583007C211yesmaximal, characteristic, complemented
5#14583003C211yesmaximal, characteristic, complemented
6#14582996C211yesmaximal, characteristic, complemented
7#14582993C211yesmaximal, characteristic, complemented
8C4×#10621885C211yesmaximal, characteristic, complemented
9SD16×Dic43C211yesmaximal, characteristic, complemented
10C4×#10621883C211yesmaximal, characteristic, complemented
11#14582940C211yesmaximal, characteristic, complemented
12#14582892C211yesmaximal, characteristic
13#103×D43C211yesmaximal, characteristic, complemented
14#14582856C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18#13063354C418yescomplemented
19C2×Dic172C2211yescharacteristic
20C2×#10621885C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621872C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24Q8×Dic43C2211yescharacteristic
25C4×Dic86—21no—
26C4×Dic86C2211yescharacteristic
27C4×Dic86C2211yescharacteristic
28#13063290—21no—
29#13063290C2211yescharacteristic
30#13063290C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32C4×C22⋊D43—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283—21no—
35#13063283C2211yescharacteristic
36#13063282—21no—
37#13063282C2211yescharacteristic
38#13063281—21no—
39C2×Dic43⋊C4—21no—
40C4⋊C4×D43C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063246C2211yescharacteristic
50#13063235C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52C8×Dic43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#97×C43C2211yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65C22×Dic43—21no—
66Q8×D43—22no—
67Q8×D43C2×C414yescomplemented
68#10621900—22no—
69#10621900C2×C414yes—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76SD16×C43C2×C414yescomplemented
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C42×C43—21no—
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86#10621885C2×C414yescomplemented
87#10621883C2×C414yescomplemented
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4D411yescharacteristic
90(C2×D43)⋊C4D411yescharacteristic
91C4⋊Dic43—21no—
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110Dic172C2×C414yescomplemented
111#10621872C2×C414yescomplemented
112C8×D43—22no—
113C23×C43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43C22×C412yes—
117D4×C43—21no—
118D4×C43C22×C412yes—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—81no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—24no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—24no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—81no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C4×D43—24no—
137C4×D43—81no—
138C4×D43C22×C412yes—
139C4×D43#4112yes—
140Dic86—21no—
141Dic86—21no—
142Dic86—24no—
143Dic86C22×C412yes—
144Dic86C22×C412yes—
145C8×C43—21no—
146C8×C43C22×C412yes—
147C43⋊C8—21no—
148C43⋊C8C22×C412yes—
149C22×C43—22no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43C4×D412yes—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C23×C411yescharacteristic
162C4×C43C2×#4111yescharacteristic
163Dic43—22no—
164Dic43—22no—
165Dic43—21no—
166Dic43—21no—
167Dic43—41no—
168Dic43—41no—
169Dic43C4×D412yes—
170#2947—431nomaximal, Sylow
171C2×C43—42no—
172C2×C43C2×C4×D411yescharacteristic
173C2×C43#57711yescharacteristic
174C2×C43#57811yescharacteristic
175D43—22no—
176C2×#137—431no—
177#520—431no—
178#519—431no—
179#441—431no—
180#441—431no—
181#440—431no—
182#440D4311yescharacteristic, complemented
183C4×Q16—431no—
184C4×Q16—431no—
185C4×SD16—431no—
186C4×SD16—431no—
187#428—431no—
188#416—431no—
189C2×#103—431no—
190#405—431no—
191C43#294711yescharacteristic, complemented, Sylow
192C2×#41—431no—
193C22×Q8—431no—
194#137—438no—
195C2×Q16—431no—
196C2×Q16—431no—
197C2×SD16—431no—
198C2×SD16C2×D4311yescharacteristic
199C2×M16—431no—
200C22×C8—431no—
201C4×Q8—431no—
202C4×Q8—431no—
203C4×Q8—431no—
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8—861no—
207C4×Q8—861no—
208C4×Q8C2×D4311yescharacteristic
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212C4×D4C2×D4311yescharacteristic
213#117—431no—
214#117—431no—
215#117—861no—
216#117—861no—
217#117—861no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—861no—
220#107—431no—
221#107C2×D4311yescharacteristic
222#106—431no—
223#106—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103C2×D4311yescharacteristic
230#102—431no—
231#102C2×D4311yescharacteristic
232#97—431no—
233#97C2×D4311yescharacteristic
234C4×C8—431no—
235C4×C8—431no—
236#41—434no—
237#41—862no—
238C2×Q8—434no—
239C2×Q8—431no—
240C2×Q8—431no—
241C2×Q8—861no—
242C2×Q8—862no—
243C2×Q8C22×D4311yescharacteristic
244C2×D4—861no—
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—431no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252Q16—434no—
253Q16—434no—
254SD16—434no—
255SD16C4×D4314yescomplemented
256M16—434no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—862no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22×D4311yescharacteristic
274C4⋊C4C22×D4311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—431no—
277C22⋊C4—431no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C42—21no—
281C42—431no—
282C42—861no—
283C42—861no—
284C42—861no—
285C42—861no—
286C42—861no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—431no—
291Q8—21no—
292Q8—432no—
293Q8—432no—
294Q8—864no—
295Q8—861no—
296Q8—861no—
297Q8C2×C4×D4312yes—
298D4—21no—
299D4—864no—
300D4C2×C4×D4312yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—431no—
306C2×C4—432no—
307C2×C4—432no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—864no—
311C2×C4—864no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4D4×D4311yescharacteristic
319C2×C4D4×D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—21no—
322C8—432no—
323C8—861no—
324C8C2×C4×D4312yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—432no—
329C22—861no—
330C22—861no—
331C22C2×D4×D4311yescharacteristic
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—432no—
338C4—862no—
339C4—862no—
340C4—861no—
341C4—861no—
342C4—1721no—
343C4—1721no—
344C4C22×C4×D4311yescharacteristic
345C4#41×D4311yescharacteristic
346C2—42no—
347C2—862no—
348C2C4×D4×D4311yescharacteristic
349C2#1458370911yescharacteristic
350C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#2947
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14583375C2semidirect
4. #14583007C2semidirect
5. #14583003C2semidirect
6. #14582996C2semidirect
7. #14582993C2semidirect
8. C4×#10621885C2semidirect
9. SD16×Dic43C2semidirect
10. C4×#10621883C2semidirect
11. #14582940C2semidirect
13. #103×D43C2semidirect
14. #14582856C2semidirect
15. C43×#440C2semidirect
18. #13063354C4semidirect
67. Q8×D43C2×C4semidirect
76. SD16×C43C2×C4semidirect
86. #10621885C2×C4semidirect
87. #10621883C2×C4semidirect
110. Dic172C2×C4semidirect
111. #10621872C2×C4semidirect
182. #440D43semidirect
191. C43#2947semidirect
255. SD16C4×D43semidirect